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Description: A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probabi

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.

1. Does the table show a probability distribution? Select all that apply.

A Yes, the table shows a probability distribution.

This is the correct answer.

B. No, the random variable x's number values are not associated with probabilities.

C. No, the random variable x is categorical instead of numerical.

D. No, the sum of all the probabilities is not equal to 1.

E. No, not every probability is between 0 and 1 inclusive.

2. Find the mean of the random variable x, or does table does not show a probability distribution?

3. Find the standard deviation of the random variable x, or does table does not show a probability distribution?

The table represents a discrete probability distribution. It shows the probability $ P(x) $ of a random variable $ x $ taking on certain values:

- When $ x = 0 $, $ P(x) = 0.091 $
- When $ x = 1 $, $ P(x) = 0.341 $
- When $ x = 2 $, $ P(x) = 0.399 $
- When $ x = 3 $, $ P(x) = 0.169 $

This table can be used to understand the likelihood of different outcomes for the random variable $ x $.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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